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MAMT 566 Algebraic Structures
Fall 2012

 Instructor: Tom Hull Time: Mondays and Wednesdays from 3:30pm - 5:20pm, starting Monday, September 17, 2012 Location: somewhere in Herman Hall This course is about algebra, viewed abstractly. That sounds scary, but it's actually wonderful! Mathematics is all about the study of patterns, and algebra represents one of the most powerful math patterns we have. That is, what happens when you have a set of objects (like numbers, maybe) and some operations you can do on them (like addition or multiplication)? What patterns emerge from such structures? That's what we will study in this class. The three basic structures that we will encounter are groups, rings, and fields. But there are other algebraic structures, like modules, that we might also take a look at. When we do this, our emphasis will be on the following: Examples: The best way to keep the terminology of abstract algebra straight in your head is by having a library of examples to draw upon, like the real number system, the integers, modular arithmetic, and symmetries. We'll do lots of examples. Applications (more examples!): If you've seen any abstract algebra before, you know that it can easily spin out of control in terms of lofty and disconnected it can feel. We will bring the subject down to earth by spending lots of time on applications. How can abstract algebra help us solve puzzles, like the sliding 15-piece puzzle, or Rubik's cube? How can it help us tie knots? How can it help us do origami? How can it help us prove that you can't trisect an angle with a straightedge and compass? Theory: There is no getting around, however, that the most powerful feature of studying abstract structures is the arsenal of theoretical tools it provides. By proving theorems about groups, rings, and fields, we learn things that can help us in all of the applications that were described above. So a big part of this course will be devoted to developing the theory, and that means theorems and proofs. Textbook: Abstract Algebra: Theory and Applications, 2011 edition, by Tom Judson, open-source textbook Yes, this book is a free book that you can download on-line. You can get it by going to the web page http://abstract.ups.edu/index.html, clicking on "Home", and then downloading the PDF of the 2011 edition. However, if you would prefer to have a hardcover copy of this book, you can get via print-on-demand at Amazon.com for only \$20. Be aware, though, that according to Tom Judson's web page, the print-on-demand version is the 2009 version, which is slightly different from the 2011 version in terms of chapter numbers, but these differences look minor. (I will probably go ahead and buy the hardcover version so that I won't have to print it out myself.) SCRATCH THAT! Tom Judson updated his web page --- the Amazon print-on-demand version IS the 2011 version, so if you get that you'll be good and everyone will be on the same page. Ha ha!   Please contact me if you have any questions! thull@wne.edu Last updated: 7/4/2012